Practical importance (RQ2)

How to demonstrate that the control solutions developed for RQ1 have also practical worth?

The most essential part of proving the practical worth of theoretically good controller is to implement it into a real HWM and conduct field experiments. Only this way can the effect of unmodeled factors (e.g., disturbances and features) be evaluated. This requires the controller to be real-time capable. In addition, there should be as few estimated values as possible (e.g., fuel consumption should be measured instead of calculating it based on other variables).

The obtained performance has to be compared with credible baselines that are preferably utilized in real HWMs of similar type. This is a challenge as the available data about these solutions is extremely scarce.

This answer is justified by discussing the features F3, F4 and F5. Experimentally Verified (F3)

Field tests are essential in the evaluation of the benefits of the developed controllers. Moreover, as the focus is on improving the fuel economy of HSDs, fuel consumption should be measured instead of predicting it with a model. Successful experimental testing also guarantees a certain level of robustness, as the utilized models are never perfectly consistent with the reality.

Both the FOC of P.II and the velocity-tracking controller of P.III were evaluated in field tests. The results verified the applicability and performance of these controllers under modelling uncertainties in a variety of different tests.

The success was demonstrated in P.II with the online fuel consumption measurement system described in Section 3.1.3. By measuring this variable, the effects of all the possible modelling errors (e.g., utilization of steady-state BSFC maps of the engine) are removed from the data. The uncertainties related to human operators were lifted in the fuel economy tests with the autonomous drive algorithm originally presented in [5].

Credible Comparison (F4)

The performance of the developed controllers should be assessed by comparing both of them with feasible textbook solutions and state-of-the-art commercial algorithms of similar applications when viable.

When evaluating the performance of the designed controller, it is a common practice to compare the obtained responses with those of other controllers. However, the lack of standardized methods together with the limited

controllers utilized as baselines are practically always devised by the researchers conducting the study. This is not that problematic if the reader knows the field well enough to assess whether the choices made are justified. Ideally, a globally optimal solution can be derived for the tested cycles.

The comparative controller utilized in the EM part of this research is devised based on a commercial algorithm (see Section 2.2.1.2 for details). However, the HSD motors with two discrete displacement settings are very rare in commercial machines. Therefore, the baseline does not exactly correspond to the commercial solution in terms of the control command of HSD motors. In addition, the minimum engine speed in P.I was set to 1,500 r/min, but in P.II and P.IV, it was 1,000 r/min. This resulted in improved energy efficiency of the baseline. In P.III, both classical state feedback and a PID controller were utilized in the experiments for com- parison purposes.

One easily interpretable baseline for EM controllers can be obtained with DP, which enables determining global optima for a specific test cycle. Nevertheless, this requires accurate information, for example about the disturbances during the cycle, which in practice prevents utilizing the method in the field experiments of P.II, as collecting such data is not a trivial matter. However, DP suffers severely from “the curse of dimensionality,” meaning that the calculation time increases substantially if the model has several states. For this reason, com- parisons against global optima were not performed in P.IV, in which the system model includes eight states and two control inputs.

Real-Time Implementable (F5)

The primary requirement for the controllers is that the information about the future should not be mandatory. This enables real-time implementation that is necessary for F3.

In order to be real-time implementable, a control algorithm has to be executable in terms of available infor- mation and computational resources. The former is usually achieved if accurate information about the future is not required. The latter depends solely on the unit in which the calculations are performed. One solution for broadening the scope of applicable units is to decrease the search space of the algorithm for faster execution. However, this will probably have an effect on the degree of optimality.

None of the controllers devised in this research require information about the future. In P.IV, predictions were made for a pre-determined time ahead, but they were always based on the current state of the system and assumed a constant velocity reference. This enabled utilizing them, for example, in human-operated machines in which the next reference value cannot be exactly known.

The controllers presented in P.II and P.III were implemented in the research platform machine described in Chapter 3. In addition, simulations of P.I were performed in real-time. Furthermore, the execution time of the FOC, discussed in P.I and P.II, can be made faster by decreasing the number of CCCs included in the search space.

The NMPC presented in P.IV is not optimized in terms of calculation time. Even with modern processing units, the current implementation is not real-time capable. However, the presented algorithm is intended for a bench- mark to which, for example, implementations including less states or state-dependent linear models can be compared.